A new model has been developed to estimate the flow stress under hot deformation conditions up to the peak of the stress-strain curves. This model is derived from the general form of hyperbolic function by introducing an additional parameter to bring the results to a more acceptable level. Stress-strain curves and the critical strain of a '304 austenitic stainless steel' are determined with an average percentage error of 1.24. The model is also used to obtain an equation which has the ability of predicting the critical strain for the onset of dynamic recrystallization. (C) 2013 Elsevier Ltd. All rights reserved.